1. Field of the Invention
This invention relates generally to seismic data processing and more particularly to a method for optimizing the spatial geometry of a seismic data-acquisition array to insure adequate data sampling and to avoid singularities.
2. Discussion of the prior Art
In the art of seismic exploration, an acoustic wavefield (a shot) is generated by an acoustic source. The wavefield propagates through the earth from a source location. The wavefield is reflected from earth layers beneath the surface whence it returns to the surface. A plurality of seismic detectors are distributed on or near the surface of the earth, remotely from the source location, along lines of survey or in large areal patches. Preferably, the detectors, which constitute discrete wavefield sampling stations, are uniformly distributed spatially so that the wavefield can be uniformly sampled both areally and temporally. The sampled data are quantized and archivally recorded for further processing.
With respect to seismic exploration in general, the ideal uniform distribution is sometimes not possible because of obstructions such as buildings, roads or other culture. In the case of marine exploration, the distribution is irregular because of errors in the assumed detector locations due to cable drift because of currents and wind or due to the presence of drilling and production platforms. The seismic data are often not only locally under-sampled, they also may be locally excessively densely sampled.
Well-known seismic dam-processing algorithms such as stacking, multi-channel filtering, dip moveout correction (DMO), prestack migration, velocity analyses, anisotropy studies, migration and wavefield extrapolation, all assume that the data are uniformly sampled. However, in operation, as has been explained, the data gathered may be irregularly sampled whether because of obstructions or to missing shots or to inoperative detectors or receivers. When such irregular or inadequately spatially sampled data are not corrected, unwanted computational artifacts may result that are superimposed upon the processed output data. Optimum computational results often can be obtained with proper design of the array geometry, that is, by optimizing the distribution of the seismic sources and receivers to minimize or eliminate singularities in the data.
U.S. Pat. No. 5,206,837, issued Apr. 27, 1993 to C. Beasley et al. and assigned to the assignee of this disclosure, addresses a method for compensating for the effects of irregular spatial sampling of seismic wavefields and is incorporated herein by reference. One of the purposes of that method is to spline or interpolate across regions of sparse data.
M. S. Egan et al. in a paper published in The Leading Edge, v. 11 , p. 37, 1991 entitled "Shooting Direction for 3-D Marine Data", points out that the direction of progress down a seismic line has an effect on the resolution of positive versus negative dips. Although they recognize the problem, they do not propose a solution.
In this disclosure, the term "operator" will be used frequently. The term is defined to mean a specific thing involved in a data-processing operation. Thus a DMO operator is a specific expression involved in applying a correction to normal moveout for dip. An operator may be expressed as a symbol indicating an operation to be performed and itself may be the subject of mathematical manipulation.
There is a need for a method for examining the proposed geometry of a seismic survey for the purpose of detecting, in particular, shadow zones and in general, finding over- or under-sampled data zones and for providing guidelines for avoiding creation of such zones ab initio by reconfiguring the array geometry.